In exterior calculus on smooth manifolds, the exterior derivative and wedge products are natural with respect to smooth maps between manifolds, that is, these operations commute with pullback. In discrete exterior calculus (DEC), simplicial cochains play the role of discrete forms, the coboundary operator serves as the discrete exterior derivative, and an antisymmetrized cup-like product provides a discrete wedge product. We show that these discrete operations in DEC are natural with respect to abstract simplicial maps. A second contribution is a new averaging interpretation of the discrete wedge product in DEC. We also show that this wedge product is the same as Wilson’s cochain product defined using Whitney and de Rham maps.

在光滑流形上的外微积分中，外导数和楔积对于流形之间的光滑映射是自然的，也就是说，这些操作可以通过回拉进行交换。在离散外微积分（DEC）中，单纯上链扮演离散形式的角色，共界算子充当离散外导数，反对称杯状积提供离散楔积。我们证明了 DEC 中的这些离散运算对于抽象单纯映射来说是自然的。第二个贡献是对 DEC 中离散楔形乘积的新平均解释。我们还表明，该楔形产品与使用 Whitney 和 de Rham 映射定义的 Wilson 协链产品相同。